Question

How do you prove `(1-cos^2)(1+cos^2)= 2sin^2-sin4`?

Answer 1

Consider as follows

`LHL`

`=(1-\cos^2x)(1+\cos^2x)`

`=(\sin^2x)(1+(1-\sin^2x))`

`=\sin^2x(2-\sin^2x)`

`=2\sin^2x-\sin^4x`

`=RHL`

Proved.